If a Monster becomes an Equip Spell, the only special thing that happens (unless otherwise stated on either the Monster being treated as an Equip Spell, or on the equipped Monster) is that it becomes bound by the game mechanics for Equip Spells - it is placed in the Spell and Trap Card Zone, rather than the Monster Card Zone, and if the equipped Monster is sent to the Graveyard then the Monster treated as an Equip Spell is also sent to the Graveyard (it is not, however, treated as still being equipped to the Monster when it it sent to the Graveyard this way).

Certain Monsters, such as those found within the Inzektor archetype, specifically state that while they are equipped with/equipped to a Monster, the equipped Monster gains X00 ATK and/or DEF (and, usually, either gains X Levels or becomes a certain Level), but this is not a game mechanic, it rather the effects of those specific cards.

Union monsters often also allow the equipped Monster to gain ATK, DEF or even a certain effect while equipped to them. However, once again this is because of the cards' particular effects, not because of game mechanics.

Adding to automatonsleuth's post, if aklys is destroyed after its monster gets destroyed or put face down, aklys's eff wont activate. it has to be sent while the monster it is equipped to is still face up such as by using legionnaire's eff or using MST.... i run dragunities so take my word for it.